Application of Absolute Nodal Coordinate Formulation in Calculation of Space Elevator System

The space elevator system is a space tether system used to solve low-cost space transportation. Its high efficiency, large load, reusability and other characteristics have broad application prospects in the aerospace field. Most of the existing mechanical models are based on “chain-bar” and a lumped mass tether model, which cannot effectively reflect the flexible behaviour of the rope of space elevator system. To establish an accurate mechanical model, the gradient deficient beam elements of the absolute nodal coordinate formulation (ANCF) are used to build the mechanical model of the space elevator system. The universal gravitation and centrifugal force in the model are derived. The calculation results of the ANCF model are compared with the results of the finite element method (FEM) and lumped mass (LM) models. The results show that the calculation results of the ANCF method are not very different from the results of the FEM and LM models in the case of axial loading. In the case of lateral loading, the calculation results of the ANCF method are basically the same as the results of the FEM and LM models, but can better reflect the local flexible deformation of the space elevator rope, and have a better calculation stability than FEM. Under the same calculation accuracy, the ANCF method can use fewer elements, and the speed of convergence is faster than the FEM and LM models.

A new thin beam element with cross-section distortion of the absolute nodal coordinate formulation

A novel modelling approach to beams with thin cross-sections is proposed in the absolute nodal coordinate formulation (ANCF), where the Lagrange interpolating and curve fitting techniques of numerical analysis are utilized for construction of the thin beam cross-section contour. Although the slope vector with respect to the coordinate line on cross-section contour is not considered in nodal coordinates, the cross-section distortion could be adequately captured through selecting an appropriate degree of polynomial. The main advantages of the present ANCF thin beam element are that the computational costs are more inexpensive than the ANCF shell element due to less generalized coordinates, there is very small amount of input data because slope vectors of the cross-section are eliminated, and the cross-sectional stress distribution may always be continuous on account of the fact that the cross-section is not discretized into a set of finite elements. Moreover, the formulations of elastic forces and Jacobian of thin laminated composite beam are also derived based on the continuum mechanics. Finally, several examples including both static and dynamic problems are performed to verify the new element and meanwhile demonstrate its general characteristics.

Numerical Investigation of Dynamics of the Flexible Riser by Applying Absolute Nodal Coordinate Formulation

In this paper, the dynamics of the flexible riser are investigated based on the absolute nodal coordinate formulation (ANCF). The stiffness, generalized elastic force, external load, and mass matrixes of the element are deduced based on the principle of energy conversion and assembled with the finite element method. The motion equation of the flexible riser is established. The influence of the environmental load conditions on the flexible riser model is studied in the MATLAB environment. Moreover, the accuracy and reliability of the programs are verified for a beam model with theoretical solutions. Finally, the static and dynamic characteristics of the flexible riser are analyzed, systematically adopting the ANCF method, which in turn proves the effectiveness and feasibility of the ANCF. Therefore, the proposed method is a powerful scheme for investigating the dynamics of flexible structures with large deformation in ocean engineering.

Validation and Analysis on Numerical Response of Super-High-Speed Railway Pantograph-Catenary Interaction Based on Experimental Test

The numerical tools can be used to facilitate the design of the railway pantograph-catenary system. The validation of the current numerical results is mostly performed at a speed slower than 350 km/h. This paper aims at the validation and analysis of the numerical results at a super-high-speed. The catenary model is constructed based on a nonlinear finite element approach employing the absolute nodal coordinate formulation. A multibody dynamics model is adopted to represent the pantograph. The measurement data are collected by an inspection vehicle equipped with an instrumented pantograph operating at 378 km/h in Chengdu-Chongqing high-speed line. Comparing the numerical simulation and the field test shows that the present pantograph-catenary model can provide reliable numerical results at 378 km/h. The numerical analysis of pantograph-catenary interaction at super-high-speed shows that the trailing pantograph performance does not comply with the assessment standard at 378 km/h. The adjustment of double-pantograph interval and messenger wire tension can effectively improve the trailing pantograph performance.

Dynamic analysis of balance rope under multiple constraints with friction

Dynamic model of balance rope under multiple constraints with friction is established via using non-equal-length element division method (NEL-EDM) based on absolute nodal coordinate formulation. Then, the natural frequency of balance rope under multiple constraints is derived by the proposed method. The KDP generalized-alpha scheme is expanded to differential algebraic equations (DAEs) with friction constraint equations and used to solve the DAEs proposed by this paper. Compared with the frequencies, lateral vibration displacements at four observation points, the analysis of the NEL-EDM is carried out by MATLAB, ANSYS, and RECURDYN software, and the feasibility of NEL-EDM is verified. The frequencies of balance rope with installed bushing constraints will occur frequency veering phenomenon when the balance rope moves up and down with the conveyance. Last, free responses of the balance rope under multiple constraints due to the effects of conveyance vertical motion, and those of in-plane excitation on forced responses of balance rope under multiple constraints with friction are investigated.